Yeah, it's unfortunate that it doesn't allow any chat once the game is finished. I usually try anticipate the final moves and send any "good game" messages just before it's over. Also, I have gotten on the computer later and put something up on an opponent's wall.
But yes, irritating that you're rendered silent after checkmate.
In the chess.com Android app, in a finished game, for some reason I can't see the chat button anymore. Is that supposed to be unavailable after a game has ended? It would be nice if I can still see the chat history (or even send additional messages, like "good game, sir" or "you were just lucky, punk!").